It has been found that in addition to cooling of the cast metal strand that is efficient and suitable from the standpoint of the process engineering, high-temperature oxidation or scaling of the metal strip plays a considerable role. Due to the very high temperature of the metal strip immediately after the metal has been discharged from the mold, the strip is subject to an intense scaling effect, which adversely affects especially the downstream process steps. Therefore, it is important to try to keep the degree of scaling as low as possible.